Q8. - Algebra 1

Question

The equation $5x+12y=240$ describes the total amount of money collected when selling x paperback books at \(5 per book and y hardback books at \)12 per book. Graph the equation using the x- and y-intercepts.

Step-by-Step Solution

Answer

The x and y intercepts by using graphing are $x=48$ and $y=20$.

Step 1. State the concept for plotting a straight line using equation.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

 

Then, algebraically,

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

 

More specifically,

 

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Step 2. Plot the points.

Graph the equation by using x and y-intercept method. First, find the x and y intercept from the equation and then plot the points on the grid and join then to complete the graph. 

Find the x-intercept, plug in $y=0$ in the equation.

$$\begin{gathered} 5x+12y=240 \\ 5x+12\left(0\right)=240\text{ [Plug in }y=0] \\ 5x=240 \\ \frac{5x}{5}=\frac{240}{5} \\ x=48 \end{gathered}$$

x-Intercept: $x=48$.

Find the y-intercept, plug in $x=0$ in the equation.

$$\begin{gathered} 5x+12y=240 \\ 5\left(0\right)+12y=240\text{ [Plug in }x=0] \\ 12y=240 \\ \frac{12y}{12}=\frac{240}{12} \\ y=20 \end{gathered}$$

y-Intercept: $y=20$.

Step 3. Plot the graph.

Graph the line $5x+12y=240$ with x and y intercepts points are (48, 0) and (0, 20).

Thus, x and y intercepts are $x=48$ and $y=20$.